Exam SRM Practice Question 5
Study guide: Exam SRM
An actuary fits an AR(1) model to 240 monthly returns on an insurer's equity portfolio. The sample autocorrelations of the returns die out after the first lag. For the residuals of the fitted model:
- every sample autocorrelation lies within the bands
\pm 2/\sqrt{240}; - the sample autocorrelations of the squared residuals are positive and well outside the bands at lags 1, 2 and 3;
- a time plot shows bursts of large residuals of either sign separated by quiet stretches, with no trend in the overall level of variability.
Which conclusion is best supported?
- A) The residuals behave like white noise, so the errors can be treated as independent with a constant variance
- B) The mean model is misspecified, and a higher autoregressive order is needed to remove the leftover autocorrelation
- C) The returns are not stationary, so they should be differenced before an autoregressive model is fitted
- D) The errors' conditional variance depends on recent squared shocks, so an ARCH model for the errors is indicated
- E) The error variance is growing steadily over time, so it should be modeled as a deterministic function of time
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